How can the phrase "Alhamdulillah (Praise be to Allah)" be a supplication (du'a) while it is a remembrance (dhikr) of Allah?

The meaning of the supplication of the people of Paradise: "Their call therein will be: 'Exalted are You, O Allah,' and their greeting therein will be: 'Peace,' and the end of their call will be: 'All praise is due to Allah, Lord of the worlds'" [Yunus: 10], is that they begin their speech with glorification (Tasbeeh) and conclude it with praise (Tahmeed). Thus, praise is the conclusion of their affair. Both praise and glorification are referred to as "supplication" (du'a), so praise is part of supplication. Supplication includes both du'a al-mas'alah (supplication of asking) and du'a al-ibadah (supplication of worship), and both are interdependent. Every du'a al-ibadah entails du'a al-mas'alah, and every du'a al-mas'alah includes du'a al-ibadah. Concluding the supplication with "All praise is due to Allah, Lord of the worlds" is the norm, but there is no objection to saying "And the end of our call is that all praise is due to Allah, Lord of the worlds."